Normal structure of the onepoint stabilizer of a doublytransitive permutation group. II
Author:
Michael E. O’Nan
Journal:
Trans. Amer. Math. Soc. 214 (1975), 4374
MSC:
Primary 20B20
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Abstract: The main result is that the socle of the point stabilizer of a doublytransitive permutation group is abelian or the direct product of an abelian group and a simple group. Under certain circumstances, it is proved that the lengths of the orbits of a normal subgroup of the one point stabilizer bound the degree of the group. As a corollary, a fixed nonabelian simple group occurs as a factor of the socle of the one point stabilizer of at most finitely many doublytransitive groups.
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 R. Brauer and M. Suzuki, On finite groups of even order whose 2Sylow group is a quaternion group, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 17571759. MR 22 #731. MR 0109846 (22:731)
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 [4]
 G. Glauberman, Central elements in corefree groups, J. Algebra 4 (1966), 403420. MR 34 #2681. MR 0202822 (34:2681)
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 , On the automorphism group of a finite group having no nonidentity normal subgroups of odd order, Math. Z. 93 (1966), 154160. MR 33 #2713. MR 0194503 (33:2713)
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 D. Gorenstein and J. H. Walter, On finite groups with dihedral Sylow 2subgroups, Illinois J. Math. 6 (1962), 553593. MR 26 #188. MR 0142619 (26:188)
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 O. Grun, Beitrage zur Gruppen theorie. I, J. Reine Angew. Math. 174 (1935), 114.
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 M. E. O'Nan, A characterization of as a permutation group, Math. Z. 127 (1972), 301314. MR 47 #310. MR 0311748 (47:310)
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 , Normal structure of the onepoint stabilizer of a doublytransitive permutation group. I. Trans. Amer. Math. Soc. 214 (1975), 4374
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 B. Shult, On the fusion of an involution in its centralizer (unplublished).
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 M. Aschbacher, Fsets and permutation groups, J. Algebra 30 (1974), 400416. MR 0347952 (50:451)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994775999420
PII:
S 00029947(75)999420
Keywords:
Doublytransitive,
permutation group,
onepoint stabilizer
Article copyright:
© Copyright 1975
American Mathematical Society
